Part one:
an amusement park ride consists of a rotating
circular platform 8.78 m in diameter from
which 10 kg seats are suspended at the end
of 3.54 m massless chains. when the system
rotates, the chains make an angle of 40.7◦ with the vertical.
the acceleration of gravity is 9.8 m/s^2.
what is the speed of each seat?
answer in units of m/s.

part two
if a child of mass 49.1 kg sits in a seat, what is
the tension in the chain (for the same angle)?
answer in units of n.

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

When a bicycle coasts uphill, it moves slower and slower as it climbs. why? a. its kinetic energy is transforming into heat energy. b. its potential energy is transforming into kinetic energy. c. its kinetic energy is transforming into potential energy and heat energy. d. its potential energy is transforming into kinetic energy and heat energy.

The electric field between square plates of a parallel-plate capacitor has magnitude e. the potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. the magnitude of the electric field between the plates is now equal to a)e b)e/4 c)e/2 d)4e e)2e